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<b>let </b><font color="Maroon">R</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="orders_2.html#L1">RelStr</a> , <font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font>, <font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font>;<br/><b>let </b><font color="Maroon">c</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>, <font color="Maroon">d</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>;<br/>





<b>assume </b><a NAME="E1:19"/><i><font color="Green">E14</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> &amp; <font color="Maroon">R</font> <a href="latsum_1.html#R1" target="_self">tolerates</a> <font color="Maroon">S</font> &amp; <font color="Maroon">R</font> is <a href="orders_2.html#V3">transitive</a> &amp; <font color="Maroon">S</font> is <a href="orders_2.html#V3">transitive</a> )
 ;<br/>

<a NAME="E2:19"/>
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R</font> <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R</font> <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">a'</font> = <font color="Maroon">a</font>, <font color="Maroon">b'</font> = <font color="Maroon">b</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="latsum_1.html#K1" target="_self">[*]</a> <font color="Maroon">S</font></span>)</span> <b>by </b><i/>;<br/>
<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:19_1"/>
<font color="Maroon">a</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">b</font>
 ;<br/><a NAME="E2:19_1"/><b>then </b>
<font color="Maroon">a'</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">b'</font>
 <b>by </b><i><a class="txt" href="latsum_1.html#E1:19"><i><font color="Green">E14</font></i></a>, </i>;<br/><b>hence </b><a NAME="E3:19_1"/>
<font color="Maroon">c</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">d</font>
 <b>by </b><i><a class="txt" href="latsum_1.html#E1:19"><i><font color="Green">E14</font></i></a>, </i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E5:19"/>
<font color="Maroon">c</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">d</font>
 ;<br/>

<a NAME="E6:19"/><b>then </b>
<font color="Maroon">a'</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">b'</font>
 
<b>by </b><i><a class="txt" href="latsum_1.html#E1:19"><i><font color="Green">E14</font></i></a>, </i>;<br/>
<b>hence </b><a NAME="E7:19"/>
<font color="Maroon">a</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="txt" href="latsum_1.html#E1:19"><i><font color="Green">E14</font></i></a>, </i>;<br/>


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